# 2. log. 5/8+ log 128/125+log 5 /2 = 0.?

$2\log (\frac{5}{8})+\log(\frac{128}{125})+log(\frac{5}{2})=0\\* We\;know\;that\;\log(\frac{a}{b})=\log a-\log b,\\*\log a^{n}=n\log a\\* and\;also,\;\log1=0\\* 2(\log 5 -\log 2^3)+\log 2^7-\log 5^3+\log 5 -\log 2\\* 2\log 5-6\log 2+7\log 2-3\log 5+\log 5 - \log 2\\* 2\log(\frac{5}{5})+7\log(\frac{2}{2})\\*\Rightarrow 0+0=0\\* Hence,\;proved.$

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